Wires $\mathrm{W}_{1}$ and $\mathrm{W}_{2}$ are made of same material having the breaking stress of $1.25 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$. $\mathrm{W}_{1}$ and $\mathrm{W}_{2}$ have cross-sectional area of $8 \times 10^{-7} \mathrm{~m}^{2}$ and $4 \times 10^{-7} \mathrm{m}^{2}$, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ______ kg. (Use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Elasticity & SHM

Wires

W_{1}

and

W_{2}

are made of same material having the breaking stress of

1.25 \times 1 0^{9} N / m^{2}

W_{1}

and

W_{2}

have cross-sectional area of

8 \times 1 0^{- 7} m^{2}

and

4 \times 1 0^{- 7} m^{2}

, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ______ kg.
(Use

g = 10 m / s^{2}

)

Answer: 40

Solution

The breaking force of a wire is its breaking stress times its area:

F_{1} = 1.25 \times 1 0^{9} \times 8 \times 1 0^{- 7} = 1000

N for

W_{1}

and

F_{2} = 1.25 \times 1 0^{9} \times 4 \times 1 0^{- 7} = 500

N for

W_{2}

. The lower wire

W_{2}

supports the

10

kg block and the pan mass

m

, so its tension is

(10 + m) g

; the upper wire

W_{1}

also supports the

20

kg block, with tension

(30 + m) g

. Safety needs

(10 + m) 10 \leq 500

, giving

m \leq 40

, and

(30 + m) 10 \leq 1000

, giving

m \leq 70

. The binding limit comes from

W_{2}

, so the maximum mass in the pan is

40

kg.

JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Integer answer

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JEE Main · 2021 · 27 Aug 2021 · Shift 2 · Elasticity & SHM

Solution

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